Vagueness, Semantic Representation and Verification

This paper claims that the vagueness inherent in gradable adjectives is a reflection of an independently-motivated, underlying measurement mechanism, called the analog magnitude system (AMS). The AMS is a language external system that can be called on to help verify sentences. Differences between positive forms of gradable adjectives like tall (1) and their comparative forms (2), in terms of vagueness, is a consequence of what the AMS is measuring: for positives it measures and compares objects, and for comparatives it measures and compares abstract units (degrees). This distinction is caused by the morpho-syntactic differences between positives and comparatives. (1) John is tall ∅/for a jockey/compared to Bill. (2) John is taller than Bill. Positives differ empirically from comparatives in at least three ways. [1,2] First, comparatives allow measure phrases to describe the difference between the two objects compared, but not positives. (3-4). (3) John is three inches taller than Bill. (4) *John is three inches tall for a jockey/compared to Bill. Second, only comparatives allow crisp judgments (5-6). Comparatives can be used to describe even minute differences, but small differences are not enough to warrant application of the positive. (5) Context: a 100 page novel and a 99 page novel a. This novel is longer than that one. b. #This novel is long compared to that one. (6) Context: a boy is 5' 1/8 " , while everyone else in his family is exactly 5' tall a. This boy is taller than everyone else in his family b. #This boy is tall for a member of his family. Third, positive adjectives even when they are accompanied by an explicit standard create compelling Sorites premises (7)-(10) [7] , but comparative adjectives (14) resist them. (7) √Anyone who is 1mm shorter than someone who is tall is also tall. (8) √Anyone who is 1mm shorter than someone who is tall for a jockey is also tall for a jockey. (9) √Anyone who is 1mm shorter than someone who is tall compared to Bill is tall compared to Bill. (10)#Anyone who is one nanometer shorter than someone who is taller than Bill is also taller than Bill. These differences are unexpected if the semantic representations of both positives and comparatives should be written in terms of degrees, or precise points on a measurements scale, as in (11-12). (11) ||John is tall|| =1 iff ∃d [john is d-tall and d > c] c = …